{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.core.pylabtools import figsize\n",
    "figsize(15, 5)\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "np.random.seed(42)\n",
    "N = 100000  # size of population\n",
    "population = pd.Series(np.random.randint(1, 11, N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = {}\n",
    "n = 30  # size of each sample\n",
    "num_samples = 500  # we are drawing 500 samples, each with size n\n",
    "for i in range(num_samples):\n",
    "    samples[i] = population.sample(n).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>...</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>...</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>...</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>...</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>30 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    0    1    2    3    4    5    6    7    8    9   ...   490  491  492  493  \\\n",
       "0     3    4    1    3    3    7    6    8    6    9 ...     4    6    5    3   \n",
       "1     2    7    6    9    9    2   10    5   10   10 ...     5    7    9    6   \n",
       "2     2    1    5    3    7    3    4    4    7    7 ...     8    1    5    8   \n",
       "3     3   10    2    6    9    7   10    3    4    2 ...     4    3    2    4   \n",
       "4     1    3    5   10   10    5    9    2    3    3 ...     2    4   10    9   \n",
       "5     5    5    6    2    1    6    9    9    3    6 ...     9    1    9    9   \n",
       "6     6    2    1    3    1    9    4    2    1    4 ...    10    7    1   10   \n",
       "7     2   10    5    4    2    7    2    1    7    1 ...     4    2    4    3   \n",
       "8     1    3    5    9   10    1    1    3    6    6 ...     8    6    9   10   \n",
       "9    10    3    5    2    1    3    1    2    1    9 ...     5    1    1    7   \n",
       "10   10    1    8    8    1    3    5    2    7    5 ...     6    7    3    9   \n",
       "11    5    2    5    6    3    5    6    5    5    3 ...     9    1    7    9   \n",
       "12    5    9    7   10    7    9    1    6    8    8 ...     8    7    1    2   \n",
       "13    9    1    6    5    1    1    3    1    9    2 ...     9    1    9   10   \n",
       "14    4    3    2    2    6    5    9    7    1    8 ...     9    7    6    9   \n",
       "15    8    8    7    2    5    3    9    4    2    6 ...     5    8    3    5   \n",
       "16    4    7    2    6    3   10    3    6    6    3 ...     4    9    8    1   \n",
       "17    7    5    1    1   10    8    8    9    4    3 ...     9    6    4    5   \n",
       "18    6    4    4    7    1    7    1    1    7    2 ...     2    1    7    1   \n",
       "19    5    8    7   10    7   10    1    4    9    5 ...     2    3   10    2   \n",
       "20   10    6    6    5    5    3    4    2    1    7 ...     6    2    7    6   \n",
       "21    8    3    9    2    3    2    6    5    5    4 ...     6    7    5    9   \n",
       "22   10    6    2    9    8    6    6    7    2    6 ...     8    1    1    5   \n",
       "23    9    5    4    9    9   10    7    1    6    2 ...     7    1    4    9   \n",
       "24    7    2    4   10    3    9    9    1    6    2 ...     6    3    4    4   \n",
       "25    5    7    2    7    5    2    1   10    1    6 ...     9    2    3    9   \n",
       "26    7    1    4    3    6    5    8    5    3    2 ...     6    6    7    4   \n",
       "27    8    2    5   10    3    3    4    6    2    5 ...     8    5    2    6   \n",
       "28    9    1    2    6    2    4    7    3    9   10 ...     2    5   10   10   \n",
       "29    8    7    3    2    3   10   10    3    7    7 ...     7    9    4    5   \n",
       "\n",
       "    494  495  496  497  498  499  \n",
       "0     4    8    3    9   10    9  \n",
       "1     3    9    9    9    2    2  \n",
       "2     4   10    8    4    9   10  \n",
       "3     5    2    5    7    8    6  \n",
       "4     1    9    3    9    5    4  \n",
       "5     7   10    2    4    5    7  \n",
       "6     9    5    9   10    8    2  \n",
       "7     4    9    3    2    1    1  \n",
       "8     7    7    6   10    8    6  \n",
       "9     4    3    8    5    1    1  \n",
       "10    5    7   10    9    1    5  \n",
       "11    6    9    1    8    6    2  \n",
       "12    9    6    7   10    5    7  \n",
       "13    7   10    6    6    6    7  \n",
       "14    4    4    9    1    3    3  \n",
       "15    2    2    2    6    2    2  \n",
       "16    8   10    4    8    9    7  \n",
       "17    6    1    7   10    2   10  \n",
       "18    8    9    5    6    6    5  \n",
       "19    8   10    4    7    4    6  \n",
       "20    8    4   10    1    9    3  \n",
       "21    7    5    9    5    2   10  \n",
       "22    8    8    3    4   10    1  \n",
       "23    3    4    3   10    2    4  \n",
       "24    8    7    8    1    3    7  \n",
       "25    2    6   10    2    6    9  \n",
       "26    6    1    1    9    8    6  \n",
       "27    1    8    6    6    1    6  \n",
       "28   10    7    8    2   10    5  \n",
       "29    6    3   10    7    2    8  \n",
       "\n",
       "[30 rows x 500 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = pd.DataFrame(samples)\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>9</th>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10.165556</td>\n",
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       "      <th>11</th>\n",
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       "      <th>16</th>\n",
       "      <td>6.450000</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>8.995556</td>\n",
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       "      <th>18</th>\n",
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       "      <th>21</th>\n",
       "      <td>8.088889</td>\n",
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       "      <th>22</th>\n",
       "      <td>8.088889</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.298889</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9.023333</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.050000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>7.623333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>5.248889</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>8.666667</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>6.422222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>470</th>\n",
       "      <td>6.195556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>471</th>\n",
       "      <td>10.048889</td>\n",
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       "    <tr>\n",
       "      <th>472</th>\n",
       "      <td>9.226667</td>\n",
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       "    <tr>\n",
       "      <th>473</th>\n",
       "      <td>6.160000</td>\n",
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       "    <tr>\n",
       "      <th>474</th>\n",
       "      <td>7.912222</td>\n",
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       "    <tr>\n",
       "      <th>475</th>\n",
       "      <td>8.693333</td>\n",
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       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>6.315556</td>\n",
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       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>9.515556</td>\n",
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       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>6.890000</td>\n",
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       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>9.645556</td>\n",
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       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>7.090000</td>\n",
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       "      <th>481</th>\n",
       "      <td>9.248889</td>\n",
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       "      <th>482</th>\n",
       "      <td>9.128889</td>\n",
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       "      <th>483</th>\n",
       "      <td>8.245556</td>\n",
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       "      <th>484</th>\n",
       "      <td>6.672222</td>\n",
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       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>4.848889</td>\n",
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       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>7.343333</td>\n",
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       "      <th>487</th>\n",
       "      <td>7.223333</td>\n",
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       "      <th>488</th>\n",
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       "      <th>489</th>\n",
       "      <td>8.626667</td>\n",
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       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>5.778889</td>\n",
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       "      <th>491</th>\n",
       "      <td>7.410000</td>\n",
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       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>8.688889</td>\n",
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       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>8.476667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>6.022222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>8.312222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>8.498889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>9.045556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>9.648889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>7.698889</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             0\n",
       "0     7.965556\n",
       "1     7.782222\n",
       "2     4.632222\n",
       "3     9.410000\n",
       "4     9.560000\n",
       "5     8.383333\n",
       "6     9.848889\n",
       "7     6.778889\n",
       "8     7.595556\n",
       "9     6.823333\n",
       "10   10.165556\n",
       "11    9.440000\n",
       "12    9.183333\n",
       "13    8.395556\n",
       "14    7.266667\n",
       "15    7.183333\n",
       "16    6.450000\n",
       "17    8.995556\n",
       "18    8.898889\n",
       "19    7.445556\n",
       "20    7.405556\n",
       "21    8.088889\n",
       "22    8.088889\n",
       "23    8.298889\n",
       "24    9.023333\n",
       "25    9.050000\n",
       "26    7.623333\n",
       "27    5.248889\n",
       "28    8.666667\n",
       "29    6.422222\n",
       "..         ...\n",
       "470   6.195556\n",
       "471  10.048889\n",
       "472   9.226667\n",
       "473   6.160000\n",
       "474   7.912222\n",
       "475   8.693333\n",
       "476   6.315556\n",
       "477   9.515556\n",
       "478   6.890000\n",
       "479   9.645556\n",
       "480   7.090000\n",
       "481   9.248889\n",
       "482   9.128889\n",
       "483   8.245556\n",
       "484   6.672222\n",
       "485   4.848889\n",
       "486   7.343333\n",
       "487   7.223333\n",
       "488   8.405556\n",
       "489   8.626667\n",
       "490   5.778889\n",
       "491   7.410000\n",
       "492   8.688889\n",
       "493   8.476667\n",
       "494   6.022222\n",
       "495   8.312222\n",
       "496   8.498889\n",
       "497   9.045556\n",
       "498   9.648889\n",
       "499   7.698889\n",
       "\n",
       "[500 rows x 1 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "biased_samples=samples.var(ddof=0).to_frame()\n",
    "biased_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
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       "      <th>9</th>\n",
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       "      <th>10</th>\n",
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       "      <th>11</th>\n",
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       "      <th>14</th>\n",
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       "      <th>15</th>\n",
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       "      <th>16</th>\n",
       "      <td>8.050850</td>\n",
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       "      <th>17</th>\n",
       "      <td>8.103333</td>\n",
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       "      <th>18</th>\n",
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       "      <th>19</th>\n",
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       "      <th>21</th>\n",
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       "      <th>22</th>\n",
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       "      <th>23</th>\n",
       "      <td>8.086944</td>\n",
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       "      <th>24</th>\n",
       "      <td>8.124400</td>\n",
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       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>8.160000</td>\n",
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       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>8.140123</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>8.036865</td>\n",
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       "      <th>28</th>\n",
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       "      <td>8.004037</td>\n",
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       "      <th>470</th>\n",
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       "      <th>473</th>\n",
       "      <td>7.953870</td>\n",
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       "    <tr>\n",
       "      <th>474</th>\n",
       "      <td>7.953782</td>\n",
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       "    <tr>\n",
       "      <th>475</th>\n",
       "      <td>7.955336</td>\n",
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       "      <th>476</th>\n",
       "      <td>7.951898</td>\n",
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       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>7.955170</td>\n",
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       "      <th>478</th>\n",
       "      <td>7.952946</td>\n",
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       "      <td>7.956472</td>\n",
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       "      <td>7.957716</td>\n",
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       "      <td>7.951319</td>\n",
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       "      <th>493</th>\n",
       "      <td>7.947964</td>\n",
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       "      <td>7.944074</td>\n",
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       "      <th>495</th>\n",
       "      <td>7.944816</td>\n",
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       "      <th>496</th>\n",
       "      <td>7.945931</td>\n",
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       "      <td>7.948139</td>\n",
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       "      <th>498</th>\n",
       "      <td>7.951548</td>\n",
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       "      <td>7.951042</td>\n",
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       "26   8.140123\n",
       "27   8.036865\n",
       "28   8.058582\n",
       "29   8.004037\n",
       "..        ...\n",
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       "\n",
       "[500 rows x 1 columns]"
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     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "biased_samples=biased_samples.expanding().mean()\n",
    "biased_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
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       "      <td>7.951898</td>\n",
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       "      <td>7.955170</td>\n",
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       "      <td>7.952946</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>7.949516</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>489</th>\n",
       "      <td>7.950898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>7.946474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>7.945384</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>7.946892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>7.947964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>7.944074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>7.944816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>7.945931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>7.948139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>7.951548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>7.951042</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     biased var estimate (divide by n)\n",
       "0                             7.965556\n",
       "1                             7.873889\n",
       "2                             6.793333\n",
       "3                             7.447500\n",
       "4                             7.870000\n",
       "5                             7.955556\n",
       "6                             8.226032\n",
       "7                             8.045139\n",
       "8                             7.995185\n",
       "9                             7.878000\n",
       "10                            8.085960\n",
       "11                            8.198796\n",
       "12                            8.274530\n",
       "13                            8.283175\n",
       "14                            8.215407\n",
       "15                            8.150903\n",
       "16                            8.050850\n",
       "17                            8.103333\n",
       "18                            8.145205\n",
       "19                            8.110222\n",
       "20                            8.076667\n",
       "21                            8.077222\n",
       "22                            8.077729\n",
       "23                            8.086944\n",
       "24                            8.124400\n",
       "25                            8.160000\n",
       "26                            8.140123\n",
       "27                            8.036865\n",
       "28                            8.058582\n",
       "29                            8.004037\n",
       "..                                 ...\n",
       "470                           7.950528\n",
       "471                           7.954974\n",
       "472                           7.957663\n",
       "473                           7.953870\n",
       "474                           7.953782\n",
       "475                           7.955336\n",
       "476                           7.951898\n",
       "477                           7.955170\n",
       "478                           7.952946\n",
       "479                           7.956472\n",
       "480                           7.954671\n",
       "481                           7.957356\n",
       "482                           7.959781\n",
       "483                           7.960372\n",
       "484                           7.957716\n",
       "485                           7.951319\n",
       "486                           7.950071\n",
       "487                           7.948582\n",
       "488                           7.949516\n",
       "489                           7.950898\n",
       "490                           7.946474\n",
       "491                           7.945384\n",
       "492                           7.946892\n",
       "493                           7.947964\n",
       "494                           7.944074\n",
       "495                           7.944816\n",
       "496                           7.945931\n",
       "497                           7.948139\n",
       "498                           7.951548\n",
       "499                           7.951042\n",
       "\n",
       "[500 rows x 1 columns]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "biased_samples.columns=['biased var estimate (divide by n)']\n",
    "biased_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11d5639e8>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "biased_samples.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.240230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.050575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.791954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9.734483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.889655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.672414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>10.188506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7.012644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>7.857471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>7.058621</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10.516092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>9.765517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>9.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>8.685057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>7.517241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>7.431034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>6.672414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>9.305747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>9.205747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>7.702299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>7.660920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>8.367816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>8.367816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.585057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9.334483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>9.362069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>7.886207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>5.429885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>8.965517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>6.643678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>470</th>\n",
       "      <td>6.409195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>471</th>\n",
       "      <td>10.395402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>472</th>\n",
       "      <td>9.544828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>473</th>\n",
       "      <td>6.372414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>474</th>\n",
       "      <td>8.185057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>475</th>\n",
       "      <td>8.993103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>6.533333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>9.843678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>7.127586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>9.978161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>7.334483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>9.567816</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>482</th>\n",
       "      <td>9.443678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>483</th>\n",
       "      <td>8.529885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>484</th>\n",
       "      <td>6.902299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>5.016092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>7.596552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>7.472414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>8.695402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>489</th>\n",
       "      <td>8.924138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>5.978161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>7.665517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>8.988506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>8.768966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>6.229885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>8.598851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>8.791954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>9.357471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>9.981609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>7.964368</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             0\n",
       "0     8.240230\n",
       "1     8.050575\n",
       "2     4.791954\n",
       "3     9.734483\n",
       "4     9.889655\n",
       "5     8.672414\n",
       "6    10.188506\n",
       "7     7.012644\n",
       "8     7.857471\n",
       "9     7.058621\n",
       "10   10.516092\n",
       "11    9.765517\n",
       "12    9.500000\n",
       "13    8.685057\n",
       "14    7.517241\n",
       "15    7.431034\n",
       "16    6.672414\n",
       "17    9.305747\n",
       "18    9.205747\n",
       "19    7.702299\n",
       "20    7.660920\n",
       "21    8.367816\n",
       "22    8.367816\n",
       "23    8.585057\n",
       "24    9.334483\n",
       "25    9.362069\n",
       "26    7.886207\n",
       "27    5.429885\n",
       "28    8.965517\n",
       "29    6.643678\n",
       "..         ...\n",
       "470   6.409195\n",
       "471  10.395402\n",
       "472   9.544828\n",
       "473   6.372414\n",
       "474   8.185057\n",
       "475   8.993103\n",
       "476   6.533333\n",
       "477   9.843678\n",
       "478   7.127586\n",
       "479   9.978161\n",
       "480   7.334483\n",
       "481   9.567816\n",
       "482   9.443678\n",
       "483   8.529885\n",
       "484   6.902299\n",
       "485   5.016092\n",
       "486   7.596552\n",
       "487   7.472414\n",
       "488   8.695402\n",
       "489   8.924138\n",
       "490   5.978161\n",
       "491   7.665517\n",
       "492   8.988506\n",
       "493   8.768966\n",
       "494   6.229885\n",
       "495   8.598851\n",
       "496   8.791954\n",
       "497   9.357471\n",
       "498   9.981609\n",
       "499   7.964368\n",
       "\n",
       "[500 rows x 1 columns]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unbiased_samples=samples.var(ddof=1).to_frame()\n",
    "unbiased_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>8</th>\n",
       "      <td>8.270881</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>8.149655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>8.364786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>8.481513</td>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>8.559859</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>8.568801</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.498697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8.431968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>8.328465</td>\n",
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       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>8.382759</td>\n",
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       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>8.426074</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>8.389885</td>\n",
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       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>8.355172</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>8.355747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>8.356272</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.365805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>8.404552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>8.441379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>8.420817</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>8.313998</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>8.336465</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>8.280038</td>\n",
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       "    <tr>\n",
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       "      <td>8.232065</td>\n",
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       "      <td>8.228142</td>\n",
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       "      <th>474</th>\n",
       "      <td>8.228051</td>\n",
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       "    <tr>\n",
       "      <th>475</th>\n",
       "      <td>8.229658</td>\n",
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       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>8.226102</td>\n",
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       "      <th>477</th>\n",
       "      <td>8.229486</td>\n",
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       "      <th>478</th>\n",
       "      <td>8.227185</td>\n",
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       "      <th>479</th>\n",
       "      <td>8.230833</td>\n",
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       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>8.228970</td>\n",
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       "      <th>481</th>\n",
       "      <td>8.231748</td>\n",
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       "      <th>482</th>\n",
       "      <td>8.234257</td>\n",
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       "      <th>483</th>\n",
       "      <td>8.234867</td>\n",
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       "      <th>484</th>\n",
       "      <td>8.232120</td>\n",
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       "      <th>485</th>\n",
       "      <td>8.225503</td>\n",
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       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>8.224211</td>\n",
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       "      <th>487</th>\n",
       "      <td>8.222671</td>\n",
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       "      <td>8.223637</td>\n",
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       "      <td>8.225067</td>\n",
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       "      <th>491</th>\n",
       "      <td>8.219363</td>\n",
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       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>8.220923</td>\n",
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       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>8.222032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>8.218008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>8.218775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>8.219929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>8.222213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>8.225739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>8.225216</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            0\n",
       "0    8.240230\n",
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       "21   8.355747\n",
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       "23   8.365805\n",
       "24   8.404552\n",
       "25   8.441379\n",
       "26   8.420817\n",
       "27   8.313998\n",
       "28   8.336465\n",
       "29   8.280038\n",
       "..        ...\n",
       "470  8.224685\n",
       "471  8.229284\n",
       "472  8.232065\n",
       "473  8.228142\n",
       "474  8.228051\n",
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       "491  8.219363\n",
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       "493  8.222032\n",
       "494  8.218008\n",
       "495  8.218775\n",
       "496  8.219929\n",
       "497  8.222213\n",
       "498  8.225739\n",
       "499  8.225216\n",
       "\n",
       "[500 rows x 1 columns]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unbiased_samples=unbiased_samples.expanding().mean()\n",
    "unbiased_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>unbiased var estimate (divide by n)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.240230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.145402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7.027586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.704310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8.141379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>8.229885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>8.509688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.322557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8.270881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>8.149655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>8.364786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>8.481513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>8.559859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>8.568801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>8.498697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8.431968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>8.328465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>8.382759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>8.426074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>8.389885</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>8.355172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>8.355747</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>8.356272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>8.365805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>8.404552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>8.441379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>8.420817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>8.313998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>8.336465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>8.280038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>470</th>\n",
       "      <td>8.224685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>471</th>\n",
       "      <td>8.229284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>472</th>\n",
       "      <td>8.232065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>473</th>\n",
       "      <td>8.228142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>474</th>\n",
       "      <td>8.228051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>475</th>\n",
       "      <td>8.229658</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>476</th>\n",
       "      <td>8.226102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>8.229486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>478</th>\n",
       "      <td>8.227185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>479</th>\n",
       "      <td>8.230833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>480</th>\n",
       "      <td>8.228970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>8.231748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>482</th>\n",
       "      <td>8.234257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>483</th>\n",
       "      <td>8.234867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>484</th>\n",
       "      <td>8.232120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>8.225503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>486</th>\n",
       "      <td>8.224211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>487</th>\n",
       "      <td>8.222671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>488</th>\n",
       "      <td>8.223637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>489</th>\n",
       "      <td>8.225067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>490</th>\n",
       "      <td>8.220491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>8.219363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>492</th>\n",
       "      <td>8.220923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>493</th>\n",
       "      <td>8.222032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>494</th>\n",
       "      <td>8.218008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>8.218775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>496</th>\n",
       "      <td>8.219929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>497</th>\n",
       "      <td>8.222213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>8.225739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>8.225216</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>500 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     unbiased var estimate (divide by n)\n",
       "0                               8.240230\n",
       "1                               8.145402\n",
       "2                               7.027586\n",
       "3                               7.704310\n",
       "4                               8.141379\n",
       "5                               8.229885\n",
       "6                               8.509688\n",
       "7                               8.322557\n",
       "8                               8.270881\n",
       "9                               8.149655\n",
       "10                              8.364786\n",
       "11                              8.481513\n",
       "12                              8.559859\n",
       "13                              8.568801\n",
       "14                              8.498697\n",
       "15                              8.431968\n",
       "16                              8.328465\n",
       "17                              8.382759\n",
       "18                              8.426074\n",
       "19                              8.389885\n",
       "20                              8.355172\n",
       "21                              8.355747\n",
       "22                              8.356272\n",
       "23                              8.365805\n",
       "24                              8.404552\n",
       "25                              8.441379\n",
       "26                              8.420817\n",
       "27                              8.313998\n",
       "28                              8.336465\n",
       "29                              8.280038\n",
       "..                                   ...\n",
       "470                             8.224685\n",
       "471                             8.229284\n",
       "472                             8.232065\n",
       "473                             8.228142\n",
       "474                             8.228051\n",
       "475                             8.229658\n",
       "476                             8.226102\n",
       "477                             8.229486\n",
       "478                             8.227185\n",
       "479                             8.230833\n",
       "480                             8.228970\n",
       "481                             8.231748\n",
       "482                             8.234257\n",
       "483                             8.234867\n",
       "484                             8.232120\n",
       "485                             8.225503\n",
       "486                             8.224211\n",
       "487                             8.222671\n",
       "488                             8.223637\n",
       "489                             8.225067\n",
       "490                             8.220491\n",
       "491                             8.219363\n",
       "492                             8.220923\n",
       "493                             8.222032\n",
       "494                             8.218008\n",
       "495                             8.218775\n",
       "496                             8.219929\n",
       "497                             8.222213\n",
       "498                             8.225739\n",
       "499                             8.225216\n",
       "\n",
       "[500 rows x 1 columns]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unbiased_samples.columns=['unbiased var estimate (divide by n)']\n",
    "unbiased_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11d31acf8>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax=unbiased_samples.plot()\n",
    "biased_samples.plot(ax=ax)\n",
    "real_population_variance=pd.Series(population.var(ddof=0), index=samples.columns)\n",
    "real_population_variance.plot()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
